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Abstract

Detection and classification of patterns which are characterized by unknown parameters and state variables, must be accomplished in conjunction with a method for estimating those quantities. Further, it is often desirable to perform this combined task in a sequential fashion. In general, the estimation and recognition must be accomplished in the presence of nonstationary observation noise.

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United States

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English (United States)

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Sequential Pattern Recognition Machine

Detection and classification of patterns which are characterized by unknown
parameters and state variables, must be accomplished in conjunction with a
method for estimating those quantities. Further, it is often desirable to perform
this combined task in a sequential fashion. In general, the estimation and
recognition must be accomplished in the presence of nonstationary observation
noise.

The present technique makes use of a feature of sequential filtering
algorithms or devices, which heretofore has been considered as detrimental.
Specifically, the technique uses the property of divergence of the innovations
produced by sequential filters, in order to solve pattern recognition problems.
This divergence occurs When the model assumed in the construction of a filter
differs from that model which generates the observations. Based on this idea, a
pattern recognition problem can be solved by passing a sequence of
observations, made on a pattern, through an optimum (Kalman-Bucy) linear filter,
which is constructed by assuming that the observations were generated by an
arbitrary one-of-N possible dynamic systems. The divergence of the resulting
innovations sequence is monitored, in order to determine if the observations are
consistent with the model assumed in the construction of the filter. The decision-
making process is based on the behavior of the innovations relative to a
prescribed set of thresholds.

Where the noise, eta(i), is zero-mean and white, with
covariance matrix R(i), and t(i) is the observation time for the
i/th/ measurement. The sequence, {X(i)}, of state vectors is assumed
to be generated by one-of-N possible processes of the form
(j)

X(i) = f(i) (t(i), X(i-1), alpha) ; j = 1, 2, ---, N (2) where
alpha is an unknown constant parameter vector. In order to solve the
pattern recognition problem, it is required to determine the value of j.

The procedure for testing the hypotheses (3) is to assume H(o) true, for the
chosen value of j. Under this assumption, and with any appropriate linearizations
of (1) and (2), each vector of the observation sequence {Y(i)} is processed
through a sequential linear filter, in order to estimate X(m) and alpha. For any
specified set of observations, the innovations (equation (9)) are collected, and a
vector of these innovations is formed. The norm of...